A summary of the topic “Probability” from Class 7 Mathematics ICSE:

Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. In probability theory, events are usually denoted by capital letters (like A, B, or C).

To calculate the probability of an event, we use the formula:

[ P(E) = frac{n(E)}{n(S)} ]

where:

– ( P(E) ) is the probability of event E,

– ( n(E) ) is the number of favorable outcomes for event E, and

– ( n(S) ) is the total number of possible outcomes in the sample space.

There are different types of events and probabilities, such as:

1. Simple Event: An event with only one possible outcome.

2. Compound Event: An event with more than one possible outcome.

3. Complementary Event: The event that an event does not occur (denoted by ( overline{A} )).

4. Independent Events: Events that do not affect each other’s probabilities.

5. Dependent Events: Events where the outcome of one event affects the outcome of another.

In practical applications, probability is used in various fields such as weather forecasting, insurance, and games of chance. Understanding probability helps in making informed decisions based on the likelihood of different outcomes.